327edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:33:18Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:33, 13 March 2026
Line 87:		Line 87:
	\| [[Mirkat]]		\| [[Mirkat]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

Francium: changed EDO intro to ED intro

2025-02-21T06:29:07Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:29, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|327~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:11, 15 January 2025

2025-01-15T18:11:27Z

← Older revision		Revision as of 18:11, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 327 factors into {{~~nowrap~~\|~~3 × 109~~}}, 327edo has [[3edo]] and [[109edo]] as its subsets.		Since 327 factors into {{factorisation\|327}}, 327edo has [[3edo]] and [[109edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\| -518 327 }}		\| {{monzo\| -518 327 }}
	\| {{mapping\| 327 518 }}		\| {{mapping\| 327 518 }}
	\| 0.3273		\| +0.3273
	\| 0.3274		\| 0.3274
	\| 8.92		\| 8.92
Line 33:		Line 33:
	\| 2109375/2097152, {{monzo\| -20 39 -18 }}		\| 2109375/2097152, {{monzo\| -20 39 -18 }}
	\| {{mapping\| 327 518 759 }}		\| {{mapping\| 327 518 759 }}
	\| 0.3608		\| +0.3608
	\| 0.2715		\| 0.2715
	\| 7.40		\| 7.40
Line 40:		Line 40:
	\| 16875/16807, 19683/19600, 2100875/2097152		\| 16875/16807, 19683/19600, 2100875/2097152
	\| {{mapping\| 327 518 759 918 }}		\| {{mapping\| 327 518 759 918 }}
	\| 0.2722		\| +0.2722
	\| 0.2807		\| 0.2807
	\| 7.65		\| 7.65
Line 47:		Line 47:
	\| 540/539, 1375/1372, 8019/8000, 2100875/2097152		\| 540/539, 1375/1372, 8019/8000, 2100875/2097152
	\| {{mapping\| 327 518 759 918 1131 }}		\| {{mapping\| 327 518 759 918 1131 }}
	\| 0.2674		\| +0.2674
	\| 0.2512		\| 0.2512
	\| 6.85		\| 6.85
Line 54:		Line 54:
	\| 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000		\| 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000
	\| {{mapping\| 327 518 759 918 1131 1210 }}		\| {{mapping\| 327 518 759 918 1131 1210 }}
	\| 0.2301		\| +0.2301
	\| 0.2441		\| 0.2441
	\| 6.65		\| 6.65
Line 87:		Line 87:
	\| [[Mirkat]]		\| [[Mirkat]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294: Partial undo

2024-11-16T12:57:46Z

Partial undo

← Older revision		Revision as of 12:57, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 48:		Line 57:
	\| 0.2441		\| 0.2441
	\| 6.65		\| 6.65
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 70:		Line 86:
	\| 10/9		\| 10/9
	\| [[Mirkat]]		\| [[Mirkat]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 03:06, 16 November 2024

2024-11-16T03:06:52Z

← Older revision		Revision as of 03:06, 16 November 2024
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 327 factors into 3 × 109, 327edo has [[3edo]] and [[109edo]] as its subsets.		Since 327 factors into {{nowrap\|3 × 109}}, 327edo has [[3edo]] and [[109edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 56:		Line 48:
	\| 0.2441		\| 0.2441
	\| 6.65		\| 6.65
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 84:		Line 70:
	\| 10/9		\| 10/9
	\| [[Mirkat]]		\| [[Mirkat]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

FloraC: Review

2024-02-21T09:47:55Z

Review

← Older revision		Revision as of 09:47, 21 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~327et~~ tempers out ~~283115520/282475249, 156250000/155649627,~~ [[16875/16807]], [[19683/19600]]~~, 95703125/95551488~~, [[250047/250000]] and [[2100875/2097152]] in the 7-limit; ~~95703125/95664294, 56723625/56689952, 55296000/55240493, 20155392/20131375, 46656/46585, 2734375/2725888, 104162436/103984375, 226492416/226474325,~~ [[540/539]]~~, 9765625/9732096, 137781/137500, 5767168/5764801, 85937500/85766121~~, 1375/1372, [[~~8019~~/~~8000~~]]~~, 134775333/134217728, 47265625/47258883~~, [[~~3025~~/~~3024~~]]~~, 160083/160000~~, 35937/35840, ~~202397184~~/~~201768035~~, 102487/102400, ~~20614528~~/~~20588575~~, ~~805255~~/~~802816~~, [[~~1771561~~/~~1769472~~]] and ~~526153617~~/~~524288000~~ in the 11-limit. It supports [[petrtri]].		327edo is [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation to the full 13-limit in its [[patent val]]. The equal temperament [[tempering out\|tempers out]] the [[semicomma]] in the 5-limit; [[16875/16807]], [[19683/19600]], [[250047/250000]], and [[2100875/2097152]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], [[8019/8000]], 35937/35840, 46656/46585, 102487/102400, 137781/137500, and 160083/160000 in the 11-limit; and [[625/624]], [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4225/4224]], and [[10648/10647]] in the 13-limit. It supports [[mirkat]], [[pnict]], and the subgroup temperament [[petrtri]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	327 factors into 3 × 109, ~~with~~ [[3edo]] and [[109edo]] as its ~~subset EDOs~~.		Since 327 factors into 3 × 109, 327edo has [[3edo]] and [[109edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-518 327}}		\| {{monzo\| -518 327 }}
	\|{{mapping\|327 518}}		\| {{mapping\| 327 518 }}
	\| 0.3273		\| 0.3273
	\| 0.3274		\| 0.3274
	\| 8.92		\| 8.92
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|2109375/2097152, {{monzo\|-20 39 -18}}		\| 2109375/2097152, {{monzo\| -20 39 -18 }}
	\|{{mapping\|327 518 759}}		\| {{mapping\| 327 518 759 }}
	\| 0.3608		\| 0.3608
	\| 0.2715		\| 0.2715
	\| 7.40		\| 7.40
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|19683/19600, ~~16875/16807, 2109375~~/2097152		\| 16875/16807, 19683/19600, 2100875/2097152
	\|{{mapping\|327 518 759 918}}		\| {{mapping\| 327 518 759 918 }}
	\| 0.2722		\| 0.2722
	\| 0.2807		\| 0.2807
	\| 7.65		\| 7.65
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|540/539, ~~3025~~/~~3024~~, 8019/8000, ~~5788125~~/~~5767168~~		\| 540/539, 1375/1372, 8019/8000, 2100875/2097152
	\|{{mapping\|327 518 759 918 1131}}		\| {{mapping\| 327 518 759 918 1131 }}
	\| 0.2674		\| 0.2674
	\| 0.2512		\| 0.2512
	\| 6.85		\| 6.85
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|540/539, 625/624, ~~3025~~/~~3024~~, 8019/8000~~, 4225/4224~~		\| 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000
	\|{{mapping\|327 518 759 918 1131 1210}}		\| {{mapping\| 327 518 759 918 1131 1210 }}
	\| 0.2301		\| 0.2301
	\| 0.2441		\| 0.2441
Line 62:		Line 62:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~*		! Generator*
	! Cents~~<br>(reduced)~~*		! Cents*
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|74\327		\| 74\327
	\|271.56		\| 271.56
	\|75/64		\| 75/64
	\|[[Orson]]		\| [[Orson]]
	\|-		\|-
	\|3		\| 3
	\|44\327		\| 44\327
	\|161.47		\| 161.47
	\|192/175		\| 192/175
	\|[[Pnict]]		\| [[Pnict]]
	\|-		\|-
	\|3		\| 3
	\|50\327		\| 50\327
	\|183.49		\| 183.49
	\|10/9		\| 10/9
	\|[[Mirkat]]		\| [[Mirkat]]
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|327}} == Theory == 327et tempers out 283115520/282475249, 156250000/155649627, 16875/16807, 19683/19600, 95703125/95551488, 250047/250000..."

2023-12-22T16:04:41Z

Created page with "{{Infobox ET}} {{EDO intro|327}} == Theory == 327et tempers out 283115520/282475249, 156250000/155649627, 16875/16807, 19683/19600, 95703125/95551488, 250047/250000..."

New page

{{Infobox ET}}
{{EDO intro|327}}

== Theory ==
327et tempers out 283115520/282475249, 156250000/155649627, [[16875/16807]], [[19683/19600]], 95703125/95551488, [[250047/250000]] and [[2100875/2097152]] in the 7-limit; 95703125/95664294, 56723625/56689952, 55296000/55240493, 20155392/20131375, 46656/46585, 2734375/2725888, 104162436/103984375, 226492416/226474325, [[540/539]], 9765625/9732096, 137781/137500, 5767168/5764801, 85937500/85766121, 1375/1372, [[8019/8000]], 134775333/134217728, 47265625/47258883, [[3025/3024]], 160083/160000, 35937/35840, 202397184/201768035, 102487/102400, 20614528/20588575, 805255/802816, [[1771561/1769472]] and 526153617/524288000 in the 11-limit. It supports [[petrtri]].

=== Odd harmonics ===
{{Harmonics in equal|327}}

=== Subsets and supersets ===
327 factors into 3 × 109, with [[3edo]] and [[109edo]] as its subset EDOs.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-518 327}}
|{{mapping|327 518}}
| 0.3273
| 0.3274
| 8.92
|-
|2.3.5
|2109375/2097152, {{monzo|-20 39 -18}}
|{{mapping|327 518 759}}
| 0.3608
| 0.2715
| 7.40
|-
|2.3.5.7
|19683/19600, 16875/16807, 2109375/2097152
|{{mapping|327 518 759 918}}
| 0.2722
| 0.2807
| 7.65
|-
|2.3.5.7.11
|540/539, 3025/3024, 8019/8000, 5788125/5767168
|{{mapping|327 518 759 918 1131}}
| 0.2674
| 0.2512
| 6.85
|-
|2.3.5.7.11.13
|540/539, 625/624, 3025/3024, 8019/8000, 4225/4224
|{{mapping|327 518 759 918 1131 1210}}
| 0.2301
| 0.2441
| 6.65
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)*
! Cents (reduced)*
! Associated Ratio*
! Temperaments
|-
|1
|74\327
|271.56
|75/64
|[[Orson]]
|-
|3
|44\327
|161.47
|192/175
|[[Pnict]]
|-
|3
|50\327
|183.49
|10/9
|[[Mirkat]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct